Modelling of flows in an oil reservoir or in an underground storage is essentially based on the application to the previously gridded reservoir (or to a portion thereof) of the well-known Darcy's law describing the flow of fluids in porous media, of material balance laws in each volume unit, of thermodynamic relations governing the evolution of the phase properties of the fluids such as viscosity, density, on initial conditions, structural closure boundary conditions and well conditions.
The model known as “Black Oil”, referred to hereafter as B.O., is one of the most commonly used models in petroleum simulation. It allows to describe a compressible three-dimensional and three-phase (water-oil-gas) flow. The petroleum effluents involved in this model are generally described by a water constituent, and two constituents for the reservoir fluid, the term constituent covering here the notion of component (as H2O for water) and the notion of pseudo-component (grouping of components). The constituents involved in this model are three: a water constituent (W), a heavy hydrocarbon constituent (H) and a light hydrocarbon constituent (V). In a B.O. type model referred to as “strict”, constituent (W) is present only in the water phase, constituent (H) is present only in the liquid hydrocarbon phase (referred to as oil or condensate), and constituent (V) is divided between the liquid and vapour hydrocarbon phases (gas phase). A B.O. model referred to as “extensive” differs from a “strict” B.O. model in that constituent (H) is divided between the liquid and vapour hydrocarbon phases. However, although the use of B.O. models is applicable to a large number of industrial cases, it is not advisable in a certain number of cases, in particular in the case of condensate gas reservoirs subjected to dry gas injection.
Another well-known simulation model, referred to as “compositional” model, is also used, wherein the hydrocarbon fluids are represented by a larger number of constituents, at least three, often more, the water constituent being present only in the aqueous phase. Modelling the flow of these more detailed fluids leads to calculating times that are all the longer as the number of constituents is great.
In order to allow the modelling calculations to be carried out within a reasonable period of time, the fluids in place are described as consisting of a number of components or pseudo-components that is much more reduced than the real number of components. Switching from a detailed representation of the fluids to a representation with a smaller number of constituents is carried out by means of “lumping” or “pseudoisation” operations. In the description hereafter, unless otherwise stated, the term “pseudoisation” is used for any method allowing to reduce the number of constituents.
Various pseudoisation methods have already been proposed for selecting and defining the pseudo-components, and the engineer often has to find a compromise between precision and calculating time (and cost). For simulation of the production of condensate gas reservoirs subjected to dry gas injection, representations with about 6 or 8 constituents are generally used, which leads to calculating times which are all the longer as it is often necessary to reduce the size of the grid cells to limit numerical errors and consequently to increase the number of grid cells. Considerable effort is devoted to the development of pseudoisation methods for use in the industry, which would allow to reduce even further the number of constituents while modelling the behaviour of the fluids with precision, and making it possible to obtain detailed compositional information. The operations allowing to predict the reservoir simulation results that would be obtained using finely detailed modelling (where the fluids are represented by a greater number of components) are known to the man skilled in the art as “delumping”.
Patent WO-00/37,898 describes a pseudoisation method applicable to compositional simulations, based on selection of a number of “dominant” base components equal to the number of pseudo-components desired at the end of the procedure. In this method, the non-dominant components are represented in all the pseudo-components, and a particular dominant component is represented in a single pseudo-component only. The mathematical transformation on which the lumping method is based allows, by inverse transformation, to obtain the detailed compositional information. The composition of a pseudo-component taken in particular can show negative molar fractions of base constituents, as in the example given in Table E7 of the patent mentioned by way of reference. It is understandable that such a representation loses a certain physical sense when a particular pseudo-component is considered individually. This may lead to robustness problems when, as it is the case in practice with gas injection, a “local” simulation result, for example in certain grid cells, shows the disappearance of one or more of the constituents used in the dynamic simulation. Besides, implementation of the invention is described as requiring many iterative calculations and a large storage space.
Earlier publications describe pseudoisation methods also applicable to compositional simulations, wherein each pseudo-component is formed by grouping together several base constituents, a particular base constituent being represented in a single pseudo-component only. Lumping can be performed according to a selection of a priori set criteria such as those given in the aforementioned patent, or by means of an optimization procedure, for example as proposed by K. Liu in the paper “Reduce the Number of Components for Compositional Reservoir Simulation”, SPE 66363, presented at the SPE Reservoir Simulation Symposium, Houston, Tex., 11-14 Feb. 2001.
A paper well-known to the man skilled in the art, written by D. E. Kenyon and G. Alda Behie, “Third SPE Comparative Solution Project: Gas Cycling of Retrograde Condensate Reservoirs”, SPE 12278, Journal of Petroleum Technology, August 1987, illustrates a situation that is not exceptional: a great disparity can be observed, for the same case study, in the compositional simulation results when the simulations are carried out with different, fluid representations, and moreover with different simulation softwares. In this paper, the number of constituents ranges from 5 to 16, and the disparity of the results is in part due to the various selections of fluid compositional representations: the general tendency observed is that the smaller the number of constituents, the more the hydrocarbon liquid (referred to as oil or condensate) saturation in a particular grid cell can be underestimated, and the more the oil recovery at the surface is then overestimated.
In order to collect the detailed compositional information during a compositional reservoir simulation, delumping methods such as those described in patent WO-99/42,937 and in the paper by C. Leibovici and J. Barker “A Method for Delumping the Results of a Compositional Reservoir Simulation” SPE 49068, presented at the SPE Annual Technical Conference and Exhibition New Orleans, 27-30 Sep. 1998, can be used. The method allows to foresee the evolution of the detailed composition in time from calculations, in particular equilibrium coefficient calculations, carried out in a compositional type simulation of fluids described by a certain reduced number of pseudo-components, the number of components being at least three.
A Black Oil type representation can be considered to result from a particular pseudoisation operation providing two pseudo-components. The detailed composition of each pseudo-component, which is not useful for construction of the representation, is not known a priori, which is not a crippling obstacle in collecting detailed compositional information, by a delumping operation. Thus, patent FR-00/09,008 describes a method allowing to foresee the evolution of the detailed composition in time from calculations carried out in a Black Oil type dynamic simulation.
The principle of the delumping stage of patents WO-99/42,937 and FR-00/09,008 is to determine, from calculations carried out during simulation, with the lumped thermodynamic representation (compositional or BO), in each grid cell and at each time interval-, coefficient ΔDo and the n coefficients ΔDp (i.e. n+1 coefficients, n being the number of parameters of the state equation) of a known general equation previously published in a paper by C. F. Leibovici, E. H. Stenby, K. Knudsen, “A Consistent Procedure for Pseudo-Component Delumping”, Fluid Phase Equilibria, 1996, 117, 225-232:
                              Ln          ⁡                      (                          K              i                        )                          =                              Δ            ⁢                                                  ⁢                          D              0                                +                                    ∑                              p                =                1                            n                        ⁢                          Δ              ⁢                                                          ⁢                              D                p                            ⁢                              Π                pi                                                                        (        1        )            where Ki is the equilibrium constant of constituent i and the IIpi are fixed parameters for characterizing constituent i in the state equation for a given thermodynamic representation.
Once coefficient ΔDo and the n coefficients ΔDp determined, they are used to calculate the equilibrium constants of the constituents of the detailed thermodynamic representation (Nrb components) by applying Equation (1) to the Nrb components with their own fixed characterization parameters in the detailed thermodynamic representation.
One of the significant points of this method is that, in the delumping stage, it is not necessary to solve the Nrb equilibrium equations associated with the state equation (equations which express the equality of the fugacities of each constituent in each phase) in the various time intervals of the dynamic flow simulation, which saves calculating time.
The paper by W. H. Goldthorpe “Simulation of Gas Injection Processes in Gas-Condensate Reservoirs Using a Binary Pseudo-Component Representation”, SPE 19470, presented at the SPE Asia-Pacific Conference, Sydney, Australia, 13-15 Sep. 1989, illustrates the simulation results that can be obtained with an advanced Black Oil modelling in the case of production of a condensate gas reservoir by means of a gas injection process. The case taken as an example comes from the aforementioned publication by D. E. Kenyon and G. Alda Behie. Considering the disparity of the results in this publication, the results obtained by W. H. Goldthorpe with a Black Oil representation, by comparison with the results of a simulation performed with a detailed representation, appear to be much more coherent, but it can be seen in FIG. 8 of the paper that the solution is not satisfactory in the revaporization stage because the oil saturation in a particular grid cell (the same as in the reference paper) is very different from the saturation of the detailed compositional prediction, and seems to be truncated of negative values during eight simulated production years.
The state of the prior art is thus such that there is no simple and robust lumping method available:    allowing to reduce to three the number of pseudo-components in compositional simulations, so as to obtain notably reduced calculating times, in particular for simulation of gas injection cases with revaporization effects, difficult to treat with a Black Oil representation,    guaranteeing a physical sense to the compositional simulation results and, consequently, to the associated delumping operation results.